Yes in the sense that they frequently play games, regardless of device, and usually for long periods of time.
Personally for me, what defines a gamer?. Someone who plays games. I think it covers more than just electronic/video games too.

Game players that pay money to purchase tokens (call it what you may), in order to advance through, rather than play their way through it, I consider to be suckers rather than Gamers. Gamers Play, Suckers Pay.

Game players whose only interaction with the Community is the "look how great I am" in game status post to Facebook or equivalent, are not really Community members, they are just players exposing their narcissistic tendencies, which is a problem with todays western society where those tendencies are encouraged. If however their post to Facebook then goes on to generate a discussion about how they achieved such and such, and they provide insight to game mechanics (whether inadvertently or via knowledge), hints or tips to other players, then that starts entry into the Community.


p.s For the Suckers Pay, this excludes paying for content (expansions, questpacks, skins, mods, etc), I am referring to Pay for Advancement.